Create two equations using the given information and then combine them into a system.
15 and 23, see solution.
Practice makes perfect
We are told that the sum of two numbers is 38 and that one number is 8 more than the other. Let's list pairs of numbers that add up to 38 and see which of them differ by 8.
First Number
Second Number
Difference
37
1
36
36
2
34
35
3
32
34
4
30
33
5
28
32
6
26
31
7
24
30
8
22
29
9
20
28
10
18
27
11
16
26
12
14
25
13
12
24
14
10
23
15
8
The pair of numbers that we are looking for is 15 and 23. We can check our solution by constructing a system of equations and solving it. Let x represent the first number and y represent the second number. We can create the first equation by remembering that these numbers add up to 38.
x+ y= 38
Next, recall that one number is 8 more than the other. Let y be the greater number. Then, if we add 8 to x, the new number will be the same as y. This will be our second equation.
x+ 8= y
Now, we can combine the two equations we created and make them into one system.
x+y=38 & (I) x+8=y & (II)
We will use the graphing method to solve this system. First we need to rewrite the equations so that both of them are in slope-intercept form.
